54 lines
1.4 KiB
Factor
54 lines
1.4 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer, Slava Pestov.
|
|
! See http://factorcode.org/license.txt for BSD license.
|
|
USING: kernel math math.ranges project-euler.common sequences ;
|
|
IN: project-euler.092
|
|
|
|
! http://projecteuler.net/index.php?section=problems&id=92
|
|
|
|
! DESCRIPTION
|
|
! -----------
|
|
|
|
! A number chain is created by continuously adding the square of the digits in
|
|
! a number to form a new number until it has been seen before.
|
|
|
|
! For example,
|
|
|
|
! 44 -> 32 -> 13 -> 10 -> 1 -> 1
|
|
! 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89
|
|
|
|
! Therefore any chain that arrives at 1 or 89 will become stuck in an endless
|
|
! loop. What is most amazing is that EVERY starting number will eventually
|
|
! arrive at 1 or 89.
|
|
|
|
! How many starting numbers below ten million will arrive at 89?
|
|
|
|
|
|
! SOLUTION
|
|
! --------
|
|
|
|
<PRIVATE
|
|
|
|
: next-link ( n -- m )
|
|
number>digits [ sq ] sigma ;
|
|
|
|
: chain-ending ( n -- m )
|
|
dup [ 1 = ] [ 89 = ] bi or [ next-link chain-ending ] unless ;
|
|
|
|
: lower-endings ( -- seq )
|
|
567 [1,b] [ chain-ending ] map ;
|
|
|
|
: fast-chain-ending ( seq n -- m )
|
|
dup 567 > [ next-link ] when 1 - swap nth ;
|
|
|
|
PRIVATE>
|
|
|
|
: euler092 ( -- answer )
|
|
lower-endings 9999999 [1,b] [ fast-chain-ending 89 = ] with count ;
|
|
|
|
! [ euler092 ] 10 ave-time
|
|
! 33257 ms ave run time - 624.27 SD (10 trials)
|
|
|
|
! TODO: this solution is not very efficient, much better optimizations exist
|
|
|
|
SOLUTION: euler092
|